PROBABILITY and MENDELIAN GENETICS NAME BACKGROUND In 1866 Gregor Mendel, an Austrian monk, published the results of his study of inheritance on garden peas. Although Mendel did not understand the mechanics of inheritance, his work became the basis for the modern study of genetics. From his studies on the inheritance of certain traits in pea plants, Mendel formulated three laws of inheritance: the law of dominance, the law of segregation and the law of independent assortment. Mendel thought that every trait was controlled by a pair of factors, which we now call genes. The law of dominance states that one gene, the dominant gene, prevents the appearance of the trait controlled by the other gene, the recessive gene. The law of segregation states that during gamete (egg and sperm) formation, the pair of genes for a trait separate, so that each gamete has only one of the genes for the trait. The law of independent assortment states that as gametes are being formed, the genes for various traits separate independently of one another. In this activity you will learn some principles of probability. You will use these principles and Mendel s law to predict the inheritance of traits. OBJECTIVES: In this activity you will: 1. Predict the probability of the occurrence of a single event. 2. Predict the probability of two independent events occurring at the same time. 3. Apply Mendel,s law to predict the occurrence of certain traits on the offspring of parents exhibiting particular traits. MATERIALS: two pennies masking tape PROCEDURES AND OBSERVATIONS: 1 http://www.nisk.k12.ny.us/departments/science/probabilitylab.htm
PART I: PROBABILITY OF THE OCCURRENCE OF A SINGLE EVENT Toss a penny 20 times. Have your partner count how many times it lands head up and how many times it lands tails up. Write the totals under the observed column for 20 toss in Table 1. The law of probability states that when a procedure can result in two equally likely outcomes (in this case, heads or tails), the probability of either outcome occurring is 1/2 or 50 percent. Using the law of probability, decide how many times out of 20 tosses you would expect heads to appear and how many times you would expect tails to appear. (Think: ½ or 50% of 20 is=?) Write your answer in the expected column for 20 tosses in Table 1. Calculate deviation by subtracting the expected number from the observed number. Record these in the deviation column for 20 tosses in Table 1. Make all numbers positive. (For example: 15-10=5 or 0-10=10) Switch with your partner and repeat this process, but toss the penny 30 times. Count how many times the heads and tails will appear. Record the observed numbers in the observed column for 30 tosses in Table 1. Calculate the expected number of heads and tails and record them in the proper column in Table 1. Then calculate the deviates, and enter these in the proper column. 2 http://www.nisk.k12.ny.us/departments/science/probabilitylab.htm
TABLE I. Probability of the Occurrence of a Single Event Observed 20Tosses Expected Deviation Observed 30Tosses Expected Deviation Observed 50Tosses Expected Deviation Observed Total Expected Deviation HEADS TAILS Switch with your partner. Repeat this process and toss the penny 50 times. Keep track of the number of heads and tails. Record the observed numbers, expected numbers and deviations in the columns for 50 tosses in Table 1. Add the observed numbers of heads and tails and the expected numbers of heads and tails from the three trials and record the totals in the Total columns in Table 1. Then calculate the deviations and record these numbers. 3 http://www.nisk.k12.ny.us/departments/science/probabilitylab.htm
PART II: Probability of Independent events Occurring Simultaneously Toss two pennies 40 times simultaneously. Have your partner keep track of how many times heads-heads, heads-tails, tails-heads, and tails-tails occur. Count tails-heads and heads-tails together. Record the numbers for each combination in the observed column in Table 2. Calculate the percent of the total that each combination (heads-heads, headstails, or tails-tails) occurred and record it in the proper column. To find the percent, divide each observed number by 40 and multiply by 100. TABLE II. Probability of Independent Events Occurring Simultaneously COMBINATIONS OBSERVED % EXPECTED % DEVIATION Heads-Heads Heads-Tails Tails-Heads Tails-Tails Total 40 100% 40 100% 4 http://www.nisk.k12.ny.us/departments/science/probabilitylab.htm
According to the law of probability, when there are four equally likely outcomes from a procedure, the probability that one of the outcomes will occur is 1/4 or 25%. We can see how this is calculated. For example, we know that in tossing two pennies, the probability off heads occurring on one penny is 1/2. The possibility of heads occurring on the other penny is also 1/2. The probability of heads occurring on both pennies in one toss is 1/2 x 1/2 = 1/4. Using the law of probability, predict the expected outcomes of tossing two pennies. Record the expected numbers in the proper column in Table 2. Calculate the percent of the total that each combination is expected to occur. Enter these numbers in the proper column. Calculate the deviation by subtracting the expected from the observed and enter your results in Table 2. PART III: Probability and Mendelian Genetics We can use the probability to predict the probability of given genetic traits appearing in the offspring of particular parents. Punnett squares can also be used to obtain these results. When gametes are formed, the pair of genes that determine a particular trait separate and one gene goes to each gamete. When fertilization occurs, a male and female gamete fuse. The resulting zygote, which develops into the new individual, now contains two genes for the trait. Which two of the parents genes appear in the zygote is a result of chance. 5 http://www.nisk.k12.ny.us/departments/science/probabilitylab.htm
In this case, we will consider the inheritance in pea plants of round and wrinkled peas. R will represent the dominant gene for round peas and r will represent the recessive gene for wrinkled peas. Put a small piece of masking tape on each side of two pennies. On one penny write R on each side. On the other penny write r on each side. Toss the pennies several times. 1. What combination of genes always appears? 2. Would the offspring with these genes be round or wrinkled? Replace the old tape with new tape. On each penny, write R on one side and r on the other side. Toss the coins simultaneously until all possible combinations of genes have appeared. 3. What combinations of genes appear? 4. For each of the combinations, would the offspring be round or wrinkled? 6 http://www.nisk.k12.ny.us/departments/science/probabilitylab.htm
CONCLUSIONS AND APPLICATIONS 1. In Part 1, what was the expected ratio of heads to tails for tosses of a single coin? Did your results always agree with the expected ratio? If not, what would be a reason for the deviation? 2. Compare the deviations from the expected for 20, 30 and 50 tosses. What seems to be the relationship between the sample size and deviation? 3. In Part II, what was the probability that tails would appear on both coins? How did you arrive at this answer? 4. What was the probability that heads-tails (or tails-hears) would appear? Show your calculations. (Hint: The probability for these two combinations must be added together because they were recorded together.) 7 http://www.nisk.k12.ny.us/departments/science/probabilitylab.htm
5. If you tossed two coins simultaneously 400 times, would you expect the deviation to be greater or less than it was tossing them 40 times? 6. In Part III, when an RR plant was crossed with an rr plant, would the offspring have round peas or wrinkled peas? 7. Which of Mendel s laws did you apply to answer question 6? 8. Complete the Punnett square for the cross of RR and rr plants. gametes gametes 8 http://www.nisk.k12.ny.us/departments/science/probabilitylab.htm
9. Complete the Punnett square for the cross Rr and Rr plants. gametes gametes 10. Draw Punnett square to illustrate a Rr and rr cross. Show the genes of the parents, the possible gametes and the types of offspring. 9 http://www.nisk.k12.ny.us/departments/science/probabilitylab.htm